Geometry - Lake County and draw the basic elements of geometry using a straightedge, ... Review formulas for circumference and area of a circle. 3. ... How can you make a conjecture

Geometry

Course Number 1206310

Lake County Schools Curriculum Map

2011-2012 Geometry Lake County Schools

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PREFACE Teams of Lake County teachers created the curriculum maps in order to ensure that all students throughout the district receive a common curriculum. The maps help ensure that all state requirements are taught and that the content is divided into teachable segments with appropriate pacing. The curriculum maps will guide your instruction but provide flexibility based on the individual needs of students. The maps are living documents and feedback is requested of teachers to ensure continuous improvement. All teachers are expected to use the curriculum maps, in conjunction with data, to drive instruction. The maps were designed for the instruction to take place by quarter. There is some flexibility within the quarters for mastery and re-teaching. The expectation is that teachers will finish the content within each quarter in its entirety. The maps have been structured in such a way as to scaffold student learning. Listed below are a few of the new or updated features common to all curriculum maps: Essential Question(s):

o Provide application of the skills/concepts o Have more than one right answer which promotes student discourse o Increase the rigor in the classroom, by changing from teacher-centered to student-centered learning o Are referred to at the beginning, middle, and end of the lesson o Require you to make a decision o Promote critical thinking and problem solving o Encourage interdependence o Are open-ended

Academic Vocabulary are:

o Unfamiliar vocabulary that are essential to understanding new content within explicit instruction o Not necessarily the bold words in the chapter. o Cumulative and continuously used throughout the year. o Integrated into word walls, a research-based strategy that will facilitate vocabulary acquisition.

Common Board Configuration Elements (specific layouts may vary by sites, but must include each of these): Purpose: For the student to know what is being taught and what the student will learn

o Date o Benchmark o Measurable, student-friendly objective o Essential Question o Bell work o Agenda (Specific daily schedule) o Homework o Exit Strategy/Card


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Lessons that infuse reading, writing, and discussion are imperative components of every subject area. There should be daily: o Teacher to student and student to student discourse utilizing academic vocabulary. o Reading and authentic writing o Writing that includes higher-order thinking o Incorporation of effective reading and writing instructional strategies

Maps are organized to include the following:

o Pacing o Objective o Essential questions, content and understanding, benchmarks, and assessment o Appendix/ resources


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Geometry

Next Generation Sunshine State Standards (NGSSS)

Math Benchmark Coding Scheme

MA. 5. A. 1. 1

Subject Grade Level Body of Knowledge Big Idea / Supporting Idea Benchmark

Body of Knowledge Key

A ~ Algebra G ~ Geometry

C ~ Calculus P ~ Probability

D ~ Discrete Mathematics S ~ Statistics

F ~ Financial Literacy T ~ Trigonometry

Math Process Benchmarks

The following benchmarks should be integrated throughout the year as a means to provide more depth of understanding of this math content. MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, working backwards, and create a table. MA.912.G.8.3 Decide whether a solution is reasonable in the context of the original situation. MA.912.G.8.4 Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture. MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.


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Geometry

MA.912.G.8.6 Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing and drawing geometric figures.

Differentiated Instruction Strategies

The following differentiated instruction strategies should be incorporated throughout the entire course:

Cooperative Groups Computer Assisted Instruction Tiered Assignments Centers Flexible Grouping Curriculum Compacting/Contracts Learning Stations Scaffolding

Hands-on Instruction Leveled Texts/Resources Teacher Led Small Groups Web Quest

Language Arts Benchmarks

The following benchmarks are new to this math course description. These benchmarks should be integrated throughout the year. LA.1112.1.6.1 and LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly. LA.1112.1.6.2 and LA.910.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text. LA.1112.1.6.5 and LA.910.1.6.5 The student will relate new vocabulary to familiar words.


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Reading Writing Discussion in the classroom everyday (50% RWD)

This means that during each class period the students should be reading, writing, and/or talking about Math for 50% of the time. Many of these overlap incorporating a combination of reading, writing, and discussion.

Reading Writing Discussion in the Math Classroom: What do these look like in the Math classroom?

What does the READING process look like?

• Modeling - reading and thinking out loud • Students in small groups or pairs • Whole group when referring to a specific portion of the text • Use of graphic organizers • Incorporation of word wall activities/vocabulary strategies • Reading word problems and translating to mathematical problem by analyzing key vocabulary words

What does the WRITING process look like?

• Journal writing • Literacy logs • Student created word problems • Written responses to word wall

activities • Written answer to essential questions • Cornell Notes • Summarizing hands-on activities • Exit cards

• Writing the steps needed to work a problem

• Quick writes • Three-column vocabulary • Graphic Organizers • Cartoons • Question stems • Math poems, jingles, or raps • Student created math stories • Reports

What does the DISCUSSION process look like?

• Student discourse – discussion among and between the students. (Could be in small group, pair share, hands-on activity)

• Student to teacher discourse - responses to open ended questions, essential questions, higher order thinking prompts, etc.

• Imbedding vocabulary terms/word wall, academic vocabulary, into the discussion


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Pacing Guide for Geometry

First Quarter Second Quarter Third Quarter Fourth Quarter I. Basics of Geometry (5 days) A. Points, Lines, and Planes B. Segments, Angles and Their Measures C. Segment and Angle Bisectors D. Angle Pair Relationships E. Introduction to Perimeter, Circumference and Area II. Reasoning and Proof (5 days) A. Patterns and Inductive Reasoning B. Conditional Statements C. Definitions and Biconditionals D. Deductive Reasoning: Using Properties From Algebra Proving Statements About Segments and Angles III. Perpendicular and Parallel Lines (5 days) A. Lines and Angles B. Parallel Lines C. Proof and Perpendicular Lines D. Lines in The Coordinate Plane: Parallel and Perpendicular IV. Congruent Triangles (6 days) A. Triangles and Angles B. Congruence and Triangles SSS, SAS, ASA, AAS C. Using Congruent Triangles D. Isosceles, Equilateral, and Right Triangles

V. Properties of Triangles (7 days) A. Perpendicular and Angle Bisectors B. Bisectors in Triangles C. Medians and Altitudes of Triangles D. The Midsegment Theorem E. Hinge Theorem VI. Quadrilaterals (6 days) A. Polygons B. Angle Measures in Polygons C. Properties of Parallelograms D. Proving Quadrilaterals are Parallelograms E. Rhombuses, Rectangles, and Squares F. Trapezoids and Kites G. Polygons in the Coordinate Plane VII. Transformations (3 days) A. Reflections B. Rotations C. Translations VIII. Similarity (5 days) A. Ratio and Proportion B. Similar Polygons C. Proving Triangles are Similar D. Proportions and Similar Triangles E. Dilations

IX. Right Triangles (5 days) A. Similar Right Triangles B. The Pythagorean Theorem and Its Converse C. Special Right Triangles D. Trigonometric Ratios and Solving Right Triangles X. Circles (4 days) A. Tangents to Circles B. Arcs and Chords C. Inscribed Angles and Other Angle Relationships D. Segment Lengths in Circles E. Equations of Circles XI. Areas of Polygons and Circles (5 days) A. Areas of Triangles and Quadrilaterals B. Areas of Regular Polygons C. Perimeters and Areas of Similar Figures D. Circumference and Arc Length E. Areas of Circles and Sectors XII. Surface Area and Volume (6 days) A. Surface Area of: Prisms, Cylinders, Pyramids, Cones, and Spheres B. Volume of: Prisms, Cylinders, Pyramids, Cones, and Spheres C. Similar Solids

1 week review and Geometry EOC XIII. Angles of Elevation and

Construction (8 days) A. Angles of Elevation and Depression B. Basic Constructions **The rest of this Quarter should be used for reteach for mastery or real-world projects..


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Geometry I. Basics of Geometry - 5 days Objectives: 1. Name and draw the basic elements of geometry using a straightedge, compass, and protractor. 2. Solve real-world problems involving distance, midpoint, perimeter, and area by applying the appropriate formula. Vocabulary: Adjacent Angles, Collinear Points, Coplanar Points, Linear Pair, Segments, Rays, Planes, Postulates, Distance Formula, Bisect

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How can real-world problems involving distance, midpoint, perimeter, and area be approached?

B. Points, Lines, and Planes 1. Defined versus undefined terms. 2. Collinear and coplanar points 3. Segments, lines and rays. 4. Intersection of geometric figures. a. segments, lines, rays b. lines and planes C. Segments, Angles and Their Measures 1. Introduce postulates (axioms) a. congruent versus equals 2. Measurement a. Find distance between two points on a number line. b. Distance Formula – to find distance between two points in the coordinate plane c. use the protractor to measure angles 3. Classify angles by their measures: acute, right, obtuse and straight D. Segment and Angle Bisectors: 1. Use compass and straightedge to a. find the midpoint of a segment b. bisect an angle 2. Midpoint Formula E. Angle Pair Relationships 1. Vertical angles

MA.912.G.8.1 MA.912.G.1.1, MA.912.G.1.3 MA.912.G.1.1, MA.912.G.1.2 MA.912.G.1.3

Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms.


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Geometry I. Basics of Geometry - 5 days Objectives: 1. Name and draw the basic elements of geometry using a straightedge, compass, and protractor. 2. Solve real-world problems involving distance, midpoint, perimeter, and area by applying the appropriate formula. Vocabulary: Adjacent Angles, Collinear Points, Coplanar Points, Linear Pair, Segments, Rays, Planes, Postulates, Distance Formula, Bisect

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment 2. Linear pair of angles 3. Complementary angles 4. Supplementary angles F. Introduction to Perimeter, Circumference and Area 1. Review formulas for area and perimeter of: a. square b. rectangle c. triangle 2. Review formulas for circumference and area of a circle. 3. Problem solving by applying areas of rectangle, square, and triangles.

MA.912.G.2.5 MA.912.G.6.5


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Geometry II. Reasoning and Proof – 5 days Objectives: 1. Make predictions based on observations using inductive reasoning.

2. Recognize and analyze conditional statements, and write inverses, converses, and contrapositives by reversing the hypothesis and conclusion and negating statements.

3. Write geometric proofs by using two-column and paragraph proofs. 4. Prove segment and angle relationships by reasoning with postulates and theorems Vocabulary: Conjecture, Counter examples, Biconditional, Conclusion, Contrapositive, Converse, Hypothesis, Inverse, Negation, Theorem, Deductive Reasoning, Two-column Proof

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How can you make a conjecture and prove that it’s true?

A. Patterns and Inductive Reasoning 1. Describe visual and number patterns. 2. Use inductive reasoning: a. make a conjecture b. find a counterexample B. Conditional Statements 1. State in if-then form 2. State the converse 3. State the inverse 4. State the contrapositive 5. Introduce the point, line and plane postulates. C. Definitions and Biconditionals 1. Restate a definition into if-then form. 2. Write definitions and postulates as Bicondtionals. (if-and-only-if form) D. Deductive Reasoning – using symbolic notation 1. Using Properties From Algebra 2. Proving Statements About Segments and Angles a. write two-column proofs b. write paragraph proofs

MA.912.G.8.4 MA.912.D.6.2, MA.912.D.6.3 MA.912.D.6.2, MA.912.D.6.3 MA.912.D.6.4



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Geometry III. Perpendicular and Parallel Lines – 5 days Objectives: 1. Identify properties of parallel and perpendicular lines 2. Learn six ways to prove lines are parallel using theorems and postulates. 3. Write an equation of a line given characteristics of parallel or perpendicular lines. Vocabulary: Skew

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How can you prove that two lines are parallel?

A. Lines and Angles 1. parallel lines and planes 2. skew lines 3. Angles formed by transversals a. corresponding angles b. alternate exterior angles c. alternate interior angles d. consecutive interior angles e. same-side interior angles B. Parallel Lines 1. With Transversals a. corresponding angles postulate b. theorems about parallel lines 2. Slope of a Line a. slope of parallel lines 3. Proving Parallel Lines 4. Properties of Parallel Lines C. Proof and Perpendicular Lines 1. Introduction to flow proof 2. Prove characteristics of perpendicular lines D. Lines in The Coordinate Plane: 1. Parallel and 2. Perpendicular a. slope of perpendicular lines

MA.912.G.1.3 MA.912.G.1.3, MA.912.G.8.5 MA.912.G.1.3, MA.912.G.8.5 MA.912.G.1.2



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Geometry IV. Congruent Triangles (6 days) Objectives: 1. Classify triangles by their sides and angles. 2. Prove triangles are congruent, given information about their sides and angles. 3. Use congruent triangles to solve real-world problems. Vocabulary: Base Angles, Congruent Triangles, Exterior Angle, Corresponding Angles, Corresponding Sides

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How do the postulates and theorem for proving triangles congruent shorten the time and work involved?

A. Triangles and Angles 1. Classify triangles by sides a. equilateral b. isosceles c. scalene 2. Classify triangles by angles a. acute b. equiangular c. right d. obtuse 3. Use angle measures of triangles a. Triangle sum theorem b. Exterior angle theorem B. Congruence and Triangles, identify: 1. SSS congruence postulate 2. SAS congruence postulate 3. ASA congruence postulate 4. AAS congruence theorem C. Using Congruent Triangles 1. Proving congruent triangles 2. Using CPCTC D. Isosceles, Equilateral, and Right Triangles 1. The Base Angle Theorem 2. Proving right triangles congruent with HL

MA912.G.2.2 MA.912.G.4.3 MA.912.G.2.3, MA.912.G.4.6 MA.912.G.4.1, MA.912.G.4.3



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Geometry V. Properties of Triangles – 7 days Objectives: 1. Use properties of special lines and segments related to triangles to synthesize problems. 2. Compare side lengths and angle measures in one or more triangles to determine their size. Vocabulary: Altitude, Centroid, Circumcenter, Concurrent, Incenter, Median, Midsegment of Triangle, Orthocenter

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Where and why do triangles occur in real-world situations, such as roofs and bridge construction?

A. Perpendicular and Angle Bisectors 1. State and apply the Perpendicular Bisector Theorem and its Converse. 2. Define: A point equidistant from 2 points. 3. State and apply the Angle Bisector Theorem and its Converse by using the definitions: a. distance from a point to a line b. a point equidistant from 2 lines. B. Bisectors in Triangles 1. State and apply the concurrency of the

Perpendicular Bisectors Theorem 2. State and apply the concurrency of angle

bisectors. C. Medians and Altitudes 1. Define and apply: Median of a triangle and the centroid. 2. Define and apply: Altitudes of triangles and the orthocenter. D. The Midsegment Theorem 1. Define: The Midsegment of a triangle. 2. State and apply: Properties of midsegments. 3. Find the perimeter of the midsegment triangle. E. The Hinge Theorem 1. Apply the Hinge Theorem

MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.5 MA.912.G.4.5 MA.912.G.4.7



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Geometry VI. Quadrilaterals – 6 days Objectives: 1. Classify special quadrilaterals according to their properties.

2. Compute angle measures and areas of polygons using appropriate theorems and formulas. 3. Write proofs about special quadrilaterals using their properties as reasons.

Vocabulary: Isosceles Trapezoid, Kite, Midsegment of a Trapezoid, Convex, Concave, Rhombus, Midpoint formula

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Where do we find polygons used in the real world and in what applications?

A. Angle Measures in Polygons 1. Investigate the interior and exterior angles of polygons. 2. Use the Polygon Interior Angle Theorem to find measures of interior angles of polygons. 3. Find the number of sides of a polygon 4. Use the Polygon Exterior Angles Theorem to find the measures of exterior angles of a polygon. 5. Apply the above theorems to regular polygons. B. Polygons 1.Define convex 2. Define non-convex (concave) 3. Define regular polygons 4. Identify sides angles, vertices, and diagonals 5. Use the interior angles of a quadrilateral theorem. C. Properties of Parallelograms 1. Introduce the 5 essential characteristics of a parallelogram D. Proving Quadrilaterals are Parallelograms 1. Learn the 6 ways to prove a quadrilateral is a parallelogram. 2. Use properties of parallelograms in

MA.912.G.2.2 MA.912.G.2.1 MA.912.G.3.1 MA.912.G.3.4



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Geometry VI. Quadrilaterals – 6 days Objectives: 1. Classify special quadrilaterals according to their properties.

2. Compute angle measures and areas of polygons using appropriate theorems and formulas. 3. Write proofs about special quadrilaterals using their properties as reasons.

Vocabulary: Isosceles Trapezoid, Kite, Midsegment of a Trapezoid, Convex, Concave, Rhombus, Midpoint formula

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment coordinate geometry. E. Rhombuses, Rectangles, and Squares 1. Distinguish between the 3 special parallelograms 2. Focus on the diagonals of the special parallelograms. F. Trapezoids and Kites 1. Contrast and compare trapezoids, isosceles trapezoids and kites. 2. Introduce the Midsegment Theorem for trapezoids. G. Polygons in the Coordinate Plane 1. Classify polygons in the coordinate plane. 2. Focus on distance, midpoint, and slope

formulas.

MA.912.G.3.2 MA.912.G.3.1, MA.G.3.2 MA.912.G.3.3


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Geometry VII. Transformations – 3 days Objectives: 1.Describe three different types of motion of geometric figures in the plane. 2. Manipulate real-world situations by applying transformations. Vocabulary: Angle of Rotation, Center of Rotation, Image, Line of Reflection, Isometry, Preimage, Vector, Initial Point, Terminal Point

kEssential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How are transformations used in such areas as: art, architecture, computer-aided design and engineering?

A. Reflections (flip) 1. Introduce terms: transformation, isometry, image, and preimage. 2. Define line of reflection 3. Demonstrate reflection in the coordinate plane. 4. Find lines of symmetry. B. Rotations (turn) 1. Define center and angle of rotation. 2. Demonstrate rotation using protractor and straightedge. 3. Describe and use rotational symmetry. C. Translations (slide or glide) 1. Use the coordinate plane to perform translations. 2. Introduce vectors a. Describe initial and terminal points. b. Define component form of a vector.

MA.912.G.2.4 MA.912.G.2.4 MA.912.G.2.4



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Geometry VIII. Similarity – 5 days Objectives: 1. Prove triangles are similar by utilizing four different methods. 2. Synthesize real-world problems by using similar polygons. Vocabulary: Means, Extremes, Geometric Mean, Dilation, Enlargement, Reduction,

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How do concepts such as ratio and proportion help bridge the gap between courses of study such as geometry, algebra, drafting, and construction?

A. Ratio and Proportion 1. Review ratio, including simplifying ratios and writing extended ratios. 2. Use proportions a. Means-Extremes property. b. Reciprocal property c. Solve proportions 3. Introduce and apply the Geometric Mean 4. Visit Real-world application of proportions B. Similar Polygons 1. Definition of similar polygons 2. Symbol of similarity (~) 3. Write a Similarity Statement 4. Compare similar polygons with shrinking and enlargement, such as on a copy machine. 5. Briefly introduce Dilations. C. Proving Triangles are Similar 1. Write a proportionality statement comparing two similar triangles. 2. Use the AA similarity postulate to prove two triangles are similar. 3. Use scale factors 4. Use the Side-Side-Side Theorem 5. Use the Side-Angle-Side Theorem 6. Use similar triangles to measure distances indirectly. D. Proportions and Similar Triangles

MA.912.G.2.3 MA.912.G.2.3 MA.912.G.2.3, MA.912.G.4.6 MA.912.G.4.5



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Geometry VIII. Similarity – 5 days Objectives: 1. Prove triangles are similar by utilizing four different methods. 2. Synthesize real-world problems by using similar polygons. Vocabulary: Means, Extremes, Geometric Mean, Dilation, Enlargement, Reduction,

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment 1. Introduce the Triangle Proportionality Theorem and its Converse. 2. Use similar triangles to determine parallelism 3. Make real-world applications of similar triangles to work such as construction. E. Dilations 1. Identify dilations 2. Apply dilations

MA.912.G.2.4


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Geometry IX. Right Triangles – 5 days Objectives: 1. Differentiate properties related to general right triangles, similar right triangles and special right triangles. 2. Apply the trigonometry ratios to right triangles to solve real world challenges. Vocabulary: Geometric Mean, Pythagorean Triple, Converse of the Pythagorean Theorem, Sine, Tangent, Cosine

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Why do right triangles get their very own branch of mathematics (trigonometry)?

A. Similar Right Triangles 1. Review simplifying square roots. 2. Investigate proportions found in right triangles. 3. Use the Geometric Mean to solve problems involving the altitude drawn to the hypotenuse of a right triangle. 4. Apply the Geometric mean to make indirect measurements. B. The Pythagorean Theorem and Its Converse 1. 2 2 2c a b= + 2. Define and find Pythagorean Triples. 3. Use the Pythagorean Theorem to find altitudes of oblique triangles, and make indirect measurements. 4. Use the Converse of the Pythagorean Theorem to classify triangles as: acute, right, or obtuse. C. Special Right Triangles: 1. 30-60-90: note the relationship between the shorter leg length and hypotenuse length and the shorter leg length and longer leg length. 2. 45-45-90: note the relationship between the leg length and the hypotenuse length. 3. Apply the special right triangles to real- world situations such as the height of a ramp.

MA.912.G.5.2 MA.912.G.5.1 MA.912.G.5.4 MA.912.G.5.4, MA.912.G.5.4



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Geometry IX. Right Triangles – 5 days Objectives: 1. Differentiate properties related to general right triangles, similar right triangles and special right triangles. 2. Apply the trigonometry ratios to right triangles to solve real world challenges. Vocabulary: Geometric Mean, Pythagorean Triple, Converse of the Pythagorean Theorem, Sine, Tangent, Cosine

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment D. Trigonometric Ratios and Solving Right

Triangles 1. Sine – opposite/hypotenuse 2. Cosine – adjacent/hypotenuse 3. Tangent – opposite/adjacent 4. Learn the ratios for 30, 45, 60 degrees. 5. Use two side lengths or 6. One side length and one acute angle measure.

MA.912.G.5.4, MA.912.T.2.1


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Geometry X. Circles – 4 days Objective: 1. Utilize arcs, angles, and segments in circles to solve real-world problems. Vocabulary: Chord, Secant, Tangent, Inscribed Angle, Intercepted Arc, Point of Tangency, Equation of a Circle in Center-radius Form, Concentric Circles, Central Angle, Minor Arcs, Major Arcs, Inscribed

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Can the properties of circles help us explain such natural occurrences as the ripples in a pond or study physical objects such as the cross section of a storage tank?

A. Tangents to Circles 1. Define: circle, diameter, radius, chord, secant, and tangent. 2. Contrast tangent lines and tangent circles by defining: point of tangency; common internal and external tangents and concentric circles. B. Arcs and Chords 1. Define: central angle, minor and major arc, and semicircle. 2. Find the degree measure of all types of arcs. 3. Use chords of circles to locate the center of a circle. 4. Know and apply the properties and theorems of chords. C. Inscribed Angles and Other Angle Relationships 1. Define: intercepted arc and measure of an inscribed angle. 2. Inscribe a polygon in a circle 3. Use tangents and chords to find the measure of arcs and angles of circles. D. Segment Lengths in Circles 1. Define: segments of a chord; tangent segment; secant and external segment. 2. Find segment lengths.

MA.912.G.6.2 MA.912.G.6.2 MA.912.G.6.4 MA.912.G.6.4



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Geometry X. Circles – 4 days Objective: 1. Utilize arcs, angles, and segments in circles to solve real-world problems. Vocabulary: Chord, Secant, Tangent, Inscribed Angle, Intercepted Arc, Point of Tangency, Equation of a Circle in Center-radius Form, Concentric Circles, Central Angle, Minor Arcs, Major Arcs, Inscribed

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment E. Equation of a Circle 1. Write the equation of a circle in center-

radius form.

MA.912.G.6.6, MA.912.G.6.7


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Geometry XI. Areas of Polygons and Circles – 5 days Objectives: 1. Find areas of triangles and quadrilaterals by identifying the appropriate formula.

2. Compare perimeters and areas of similar figures using scale factor and ratio. 3. Calculate circumference and area of circles. 4. Analyze the arc length of a circle and area of a sector of a circle using angle measure and circumference and area formulas. Vocabulary: Altitude, Apothem, Arc Length, Equiangular, Regular, Sector of a Circle, Segment of a Circle

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment How do perimeters and areas of similar polygons compare?

A. Areas of Triangles and Quadrilaterals 1. Review the area formulas for rectangle, parallelogram, and triangle. 2. Review the formula for the area of a trapezoid. 3. Introduce the formulas for areas of kites and rhombuses. B. Areas of Regular Polygons 1. Introduce the formula for the area of an Equilateral Triangle. 2. Define: Center, radius, apothem, and central angle of a regular polygon. 3. Know and use the formula for area of a regular polygon (A= ½ aP) C. Perimeters and Areas of Similar Figures 1. Review perimeter and area of polygons 2. Introduce the Area of Similar Polygons Theorem a. Emphasize the relationships between the scale factor and the ratio of the perimeters of the similar polygons. b. Emphasize the relationships between the scale factor and the ratio of the areas of the similar polygons. D. Circumference and Arc Length 1. Review circumference of a circle.

MA.912.G.2.5 MA.912.G.2.5 MA.912.G.4.4, MA.912.G.2.7 MA.912.G.6.2

Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies display the connection between the various vocabulary terms.


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Geometry XI. Areas of Polygons and Circles – 5 days Objectives: 1. Find areas of triangles and quadrilaterals by identifying the appropriate formula.

2. Compare perimeters and areas of similar figures using scale factor and ratio. 3. Calculate circumference and area of circles. 4. Analyze the arc length of a circle and area of a sector of a circle using angle measure and circumference and area formulas. Vocabulary: Altitude, Apothem, Arc Length, Equiangular, Regular, Sector of a Circle, Segment of a Circle

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment 2. Use circumference to explain arc length; contrast this with “arc measure.” E. Areas of Circles and Sectors 1. Review area of a circle 2. Use area of a circle to explain area of a sector of a circle.

MA.912.G.6.4


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Geometry XII. Surface Area and Volume – 6 days Objective: 1. Calculate the surface area and volume of various solids; then apply those techniques to real-world problems. Vocabulary: Base, Cross Section, Hemisphere, Lateral Area, Lateral Faces,

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Can you compare the similarities and differences between surface area and volume?

A. Surface Area of: Prisms, Cylinders, Pyramids, Cones, and Spheres 1. Define: prism, base of a prism, lateral face, right prism, oblique prism. a. Distinguish between lateral area and surface area of a prism. 2. Define: cylinder, right cylinder. a. Distinguish between lateral area and surface area of a cylinder 3. Define pyramid, regular pyramid, slant height. a. Distinguish between lateral area and surface area of a pyramid. 4. Define: cone, right cone, lateral surface. a. Distinguish between lateral area and surface area of a cone. 5. Define: sphere, center and radius of a sphere. a. Explain why a sphere has only surface area and no lateral area. B. Volume of: Prisms, Cylinders, Pyramids, Cones, and Spheres 1. Define: volume of a solid. 2. Use the formulas for volume of the solids. 3. Introduce Cavalieri’s Principle; the Volume Congruence Postulate and the Volume Addition Postulate.

MA.912.G.7.1, MA.912.G.7.2, MA.912.G.7.4, MA.912.G.7.5, MA.912.G7.7 MA.912.G.7.4, MA.912.G.7.5, MA.912.G.7.7



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Geometry XII. Surface Area and Volume – 6 days Objective: 1. Calculate the surface area and volume of various solids; then apply those techniques to real-world problems. Vocabulary: Base, Cross Section, Hemisphere, Lateral Area, Lateral Faces,

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment C. Similar Solids 1. Find and use the scale factor of similar Solids.

MA.912.G.2.7, MA.912.G.7.6


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Geometry XIII. – Angles of Elevation and Construction (8 days) Objectives: 1. Apply the trigonometry ratios to right triangles to solve real world challenges. 2. Basic Construction Vocabulary: Angle of Depression, Angle of Elevation, Straightedge, Compass, Construction,

Essential Questions Essential Content & Understandings Essential Skills & Benchmarks Assessment Why do you use angles of elevation and depression to solve problems?

A. Angles of Elevation and Depression 1. Define and apply angle of elevation and angle of depression. 2. Apply right triangle trigonometry to real- world situations such as height of a cliff, tower, or airplane. B. Construction 1. Define and use tools of construction 2. Basic Constructions 3. Construction of parallel and perpendicular lines

MA.912.G.5.4, MA.912.T.2.1 MA.912.G.1.2, MA.912.G.4.1



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Geometry Curriculum Map Appendix for High Schools

Scope and Sequence Correlated to Textbook Pages

State Approved Course Description FCAT Math Tested Benchmarks

Vocabulary


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Scope and Sequence Correlated to Prentice Hall Geometry and NGSSS

Topic Chapter – Section, Resources NGSSS First Nine Weeks I. Basics of Geometry – (5 days) A. Points, Lines, and Planes 1-2, Lines in Geometry http://illuminations.nctm.org/ActivityDetail.aspx?ID=22 MA.912.G.8.1 B. Segments, Angles and Their Measures 1-3, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.1.1

1-7, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.1.1 C. Segment and Angle Bisectors 1-4 MA.912.G.1.3 1-5, Lines in Geometry http://illuminations.nctm.org/ActivityDetail.aspx?ID=22 MA.912.G.1.2 D. Angle Pair Relationships 1-5 MA.912.G.1.3

E. Introduction to Perimeter, 1-8, Perimeter Explorer MA.912.G.2.5

Circumference and Area http://www.shodor.org/interactivate/activities/PerimeterExplorer/ MA.912.G.6.5 II. Reasoning and Proof – (5 days)

A. Patterns and Inductive Reasoning 2-1, Pattern Generator http://www.shodor.org/interactivate/activities/PatternGenerator/ MA.912.G.8.4 B. Conditional Statements 2-2 MA.912.D.6.2 MA.912.D.6.3

C. Definitions and Biconditionals 2-3 MA.912.D.6.2 MA.912.D.6.3


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http://illuminations.nctm.org/ActivityDetail.aspx?ID=22




http://www.shodor.org/interactivate/activities/PerimeterExplorer/

http://www.shodor.org/interactivate/activities/PatternGenerator/

D. Deductive Reasoning 2-4 MA.912.D.6.4 III. Perpendicular and Parallel Lines – (5 days) A. Lines and Angles 3-1, Angles http://www.shodor.org/interactivate/activities/Angles/ MA.912.G.1.3 B. Parallel Lines 3-2, 3-3 MA.912.G.1.3 MA.912.G.8.5

C. Proof and Perpendicular Lines 3-4 MA.912.G.1.3 MA.912.G.8.5

D. Lines in the Coordinate Plane 3-8 MA.912.G.1.2 IV. Congruent Triangles – (6 days) A. Triangles and Angles 3-5, Cutting Corners http://illuminations.nctm.org/ActivityDetail.aspx?ID=7 MA.912.G.2.2 B. Congruence and Triangles 4-2, 4-3 MA.912.G.4.3

C. Using Congruent Triangles 4-4 MA.912.G.2.3 MA.912.G.4.6 D. Isosceles, Equilateral, Right Triangles 4-5, Isosceles Triangle Investigation MA.912.G.4.1 http://illuminations.nctm.org/ActivityDetail.aspx?ID=88 MA.912.G.4.3 Triangle Classification Game http://www.uff.br/cdme/jct/jct-html/jct-en.html 4-6 Second Nine Weeks V. Properties of Triangles – (7 days) A. Perpendicular and Angle Bisectors 5-2, Lines in Geometry http://illuminations.nctm.org/ActivityDetail.aspx?ID=22 MA.912.G.4.2 B. Bisectors in Triangles 5-3, Half Angle http://illuminations.nctm.org/ActivityDetail.aspx?ID=157 MA.912.G.4.2


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http://www.shodor.org/interactivate/activities/Angles/



http://www.uff.br/cdme/jct/jct-html/jct-en.html



C. Medians and Altitudes of Triangles 5-4, Lines in Geometry http://illuminations.nctm.org/ActivityDetail.aspx?ID=22 MA.912.G.4.5 In Search of Euler’s Line Resource

D. The Midsegment Theorem 5-1 MA.912.G.4.5 E. The Hinge Theorem 5-7 MA.912.G.4.7 VI. Quadrilaterals – (6 days)

A. Polygons Pgs. 65-66 MA.912.G.2.1 B. Angle Measures in Polygons 6-1 MA.912.G.2.2

C. Properties of Parallelograms 6-2, Parallelogram Exploration MA.912.G.3.1 http://illuminations.nctm.org/ActivityDetail.aspx?ID=162 D. Proving Quadrilaterals are Parallelograms 6-3 MA.912.G.3.4 E. Rhombuses, Rectangles, and Squares 6-4, Diagonals to Quadrilaterals II MA.912.G.3.2 http://illuminations.nctm.org/ActivityDetail.aspx?ID=149 F. Trapezoids and Kites 6-6 MA.912.G.3.1 MA.912.G.3.2 Geometry PROMISE Module 5 G. Polygons in the Coordinate Plane 6-7, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA912.G.3.3 VII. Transformations – (3 days) A. Reflections 9-2, Covering the Plane with Reptiles MA.912.G.2.4 http://illuminations.nctm.org/LessonDetail.aspx?id=L251 B. Rotations 9-3, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.2.4 C. Translations 9-1, Shape Cutter http://illuminations.nctm.org/ActivityDetail.aspx?ID=72 MA.912.G.2.4 Transmographer http://www.shodor.org/interactivate/activities/Transmographer/


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http://illuminations.nctm.org/LessonDetail.aspx?id=L251



http://www.shodor.org/interactivate/activities/Transmographer/

Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 VIII. Similarity – (5 days) A. Ratio and Proportion 7-1, MA.912.G.2.3 B. Similar Polygons 7-2 MA.912.G.2.3 C. Proving Triangles are Similar 7-3 MA.912.G.2.3 MA.912.G.4.6 D. Proportions and Similar Triangles 7-5 MA.912.G.4.5 E. Dilations 9-5, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.2.4

Third Nine Weeks IX. Right Triangles – (5 days) A. Similar Right Triangles 7-4 MA.912.G.5.2 B. The Pythagorean Theorem and Its Converse 8-1, Pythagorean Explorer MA.912.G.5.1 Geometry PROMISE Module 4

http://www.shodor.org/interactivate/activities/PythagoreanExplorer/ MA.912.G.5.4 C. Special Right Triangles 8-2 MA.912.G.5.3 MA.912.G.5.4 D. Trigonometric Ratios and Solving 8-3 MA.912.T.2.1

Right Triangles MA.912.G.5.4 X. Circles – (4 days) A. Tangents to Circles 12-1, Distance to Horizon http://illuminations.nctm.org/ActivityDetail.aspx?ID=150 MA.912.G.6.2


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http://www.shodor.org/interactivate/activities/PythagoreanExplorer/


B. Arcs and Chords 12-2, Power of a Point http://illuminations.nctm.org/ActivityDetail.aspx?ID=122 MA.912.G.6.2 C. Inscribed Angles and Other 12-3 MA.912.G.6.4 Angle Relationships D. Segment Lengths in Circles 12-4 MA.912.G.6.4 E. Equations of Circles 12-5, MA.912.G.6.6 Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.6.7 XI. Areas of Polygons and Circles – (5 days) A. Areas of Triangles and Quadrilaterals 10-1, 10-2 MA.912.G.2.5 B. Areas of Regular Polygons 10-3 MA.912.G.2.5 C. Perimeters and Areas of Similar Figures 10-4, Scale Factor http://illuminations.nctm.org/ActivityDetail.aspx?ID=176 MA.912.G.2.7 Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.4.4

D. Circumference and Arc Length 10-6, Circle Graph http://www.shodor.org/interactivate/activities/CircleGraph/ MA.912.G.6.2 E. Areas of Circles and Sectors 10-7, Pie Chart http://www.shodor.org/interactivate/activities/PieChart/ MA.912.G.6.4 XII. Surface Area and Volume – (6 days) A. Surface Areas of: Prisms, Cylinders, 11-2, 11-3, 11-6, Pyramids, Cones, and Spheres Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.7.1 A Plethora of Polyhedra http://www.uff.br/cdme/pdp/pdp-html/pdp-en.html MA.912.G.7.2 Isometric Drawing Tool http://illuminations.nctm.org/ActivityDetail.aspx?ID=125 MA.912.G.7.5 Tetrahedral Kites http://illuminations.nctm.org/LessonDetail.aspx?id=L639 MA.912.G.7.7 B. Volumes of: Prisms, Cylinders 11-4, 11-5, 11-6, MA.912.G.7.4


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http://www.shodor.org/interactivate/activities/CircleGraph/

http://www.shodor.org/interactivate/activities/PieChart/


http://www.uff.br/cdme/pdp/pdp-html/pdp-en.html



Pyramids, Cones, and Spheres Surface Area and Volume MA.912.G.7.5 http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/ MA.912.G.7.7 Tetrahedral Kites http://illuminations.nctm.org/LessonDetail.aspx?id=L639 C. Similar Solids 11-7, Dynamic Paper http://illuminations.nctm.org/ActivityDetail.aspx?ID=205 MA.912.G.2.7 MA.912.G.7.6 Fourth Nine Weeks 1 week review and Geometry EOC XIII. Angles of Elevation and Constructions – (8 days) A. Angles of Elevation and Depression 8-4 MA.912.T.2.1 MA.912.G.5.4 B. Basic Constructions 1.6 MA.912.G.1.2 3.6 MA.912.G.4.1 The rest of this quarter reteach for mastery or work real-world projects. This curriculum map is designed to cover the core curriculum for your math course. If your students are not successful per the specifications of RtI please use the RtI materials provided with your textbook, for Intensive Math classes, or other additional math resources that are available at your school for RtI interventions.


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http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/



State Approved Geometry Course Description Course Code 1206310 Course Category 6-12

Subject Area Mathematics Course Type Core Course Title Geometry Course Level 2 Course Length Full Year Credit Description 1

Abbreviated Title Geometry

RELATED BENCHMARKS (51) : Scheme Descriptor

LA.1112.1.6.1 The student will use new vocabulary that is introduced and taught directly;

LA.1112.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text;

LA.1112.1.6.5 The student will relate new vocabulary to familiar words;

LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly;

LA.910.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text;

LA.910.1.6.5 The student will relate new vocabulary to familiar words;


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MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement

MA.912.D.6.3 Determine whether two propositions are logically equivalent.

MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid.

MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems.

MA.912.G.1.2 Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used.

MA.912.G.1.3 Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.

MA.912.G.2.1 Identify and describe convex, concave, regular, and irregular polygons.

MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used.

MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems.

MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.

MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).

MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.


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MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.

MA.912.G.3.2 Compare and contrast special quadrilaterals on the basis of their properties.

MA.912.G.3.3 Use coordinate geometry to prove properties of congruent, regular and similar quadrilaterals.

MA.912.G.3.4 Prove theorems involving quadrilaterals.

MA.912.G.4.1 Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

MA.912.G.4.2 Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter.

MA.912.G.4.3 Construct triangles congruent to given triangles.

MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas.

MA.912.G.4.5 Apply theorems involving segments divided proportionally.

MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse.


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MA.912.G.5.2 State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

MA.912.G.5.3 Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems.

MA.912.G.5.4 Solve real-world problems involving right triangles.

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

MA.912.G.6.6 Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

MA.912.G.6.7 Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.

MA.912.G.7.1 Describe and make regular, non-regular, and oblique polyhedra and sketch the net for a given polyhedron and vice versa.

MA.912.G.7.2 Describe the relationships between the faces, edges, and vertices of polyhedra.

MA.912.G.7.4 Identify chords, tangents, radii, and great circles of spheres

MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids.

MA.912.G.7.6 Identify and use properties of congruent and similar solids.


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MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common geometric solids.

MA.912.G.8.1 Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates and theorems.

MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

MA.912.G.8.3 Determine whether a solution is reasonable in the context of the original situation.

MA.912.G.8.4 Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.

MA.912.G.8.6 Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing and drawing geometric figures.

MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles.


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Geometry End-of-Course Assessment Appendix B

MATHEMATICS CONTENT ASSESSED ON THE GEOMETRY EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK

DRAFT Geometry EOC Test Item Specifications Florida Department of Education | B–1

Geometry End-of-Course Assessment Body of Knowledge Discrete Mathematics Standard 6 Logic Develop an understanding of the fundamentals of propositional logic, arguments, and methods of proof. MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement.

Also assesses MA.912.D.6.3.

MC

MA.912.D.6.3 Determine whether two propositions are logically equivalent.

Assessed with MA.912.D.6.2.

MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid.

Assessed with MA.912.G.3.4 and MA.912.G.4.6.

Body of Knowledge Geometry Standard 1 Points, Lines, Angles, and Planes Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints

of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, construct lines and angles, explaining and justifying the processes used.

MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems.

MC, FR

MA.912.G.1.3 Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.

MC, FR

Prior Knowledge: Items may require the student to apply mathematical knowledge described in the NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation.


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Geometry End-of-Course Assessment Body of Knowledge Geometry Standard 2 Polygons Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and

concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geometry to algebra by using coordinate geometry to determine transformations. Use algebraic reasoning to determine congruence, similarity, and symmetry. Create and verify tessellations of the plane using polygons.

MA.912.G.2.1 Identify and describe convex, concave, regular, and irregular polygons.

Assessed with MA.912.G.2.3.

MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons, justifying the method used.

MC, FR

MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical or real-world problems.

Also assesses MA.912.G.2.1, MA.912.G.4.1, MA.912.G.4.2,

MA.912.G.4.4, and MA.912.G.4.5.

MC, FR

MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.

MC, FR

MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).

Also assesses MA.912.G.2.7.

MC, FR MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.




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Geometry End-of-Course Assessment Body of Knowledge Geometry Standard 3 Quadrilaterals Classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite, etc.). Relate geometry to algebra

by using coordinate geometry to determine regularity, congruence, and similarity. Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas, and prove theorems involving quadrilaterals.

MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.


MA.912.G.3.2 Compare and contrast special quadrilaterals on the basis of their properties.


MA.912.G.3.3 Use coordinate geometry to prove properties of congruent, regular and similar quadrilaterals.

MC

MA.912.G.3.4 Prove theorems involving quadrilaterals.

Also assesses MA.912.D.6.4, MA.912.G.3.1, MA.912.G.3.2,

and MA.912.G.8.5.

MC, FR

Standard 4 Triangles Identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). Define and construct altitudes, medians,

and bisectors, and triangles congruent to given triangles. Prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Understand and apply the inequality theorems of triangles.

MA.912.G.4.1 Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.


MA.912.G.4.2 Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter.


MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas.


MA.912.G.4.5 Apply theorems involving segments divided proportionally.


MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Also assesses MA.912.D.6.4

and MA.912.G.8.5.

MC Prior Knowledge: Items may require the student to apply mathematical knowledge described in the NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation.


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Geometry End-of-Course Assessment Body of Knowledge Geometry Standard 4 Triangles Identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). Define and construct altitudes, medians,

and bisectors, and triangles congruent to given triangles. Prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Understand and apply the inequality theorems of triangles.

MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

MC

.

Standard 5 Right Triangles Apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles

with special angle relationships. Use special right triangles to solve problems using the properties of triangles. MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse.


MA.912.G.5.2 State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.


MA.912.G.5.3 Use special right triangles (30°-60°-90° and 45°-45°-90°) to solve problems.


MA.912.G.5.4 Solve real-world problems involving right triangles.

Also assesses MA.912.G.5.1, MA.912.G.5.2, and

MA.912.G.5.3.

MC, FR



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Geometry End-of-Course Assessment Body of Knowledge Geometry Standard 6 Circles Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions and prove theorems

related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.


MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).


MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Also assesses MA.912.G.6.2 and MA.912.G.6.4.

MC, FR

MA.912.G.6.6 Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.


MC

MA.912.G.6.7 Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.


Standard 7 Polyhedra and Other Solids Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships

among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids and understand the properties of congruent and similar solids.

MA.912.G.7.1 Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice versa.


MC, FR

MA.912.G.7.2 Describe the relationships between the faces, edges, and vertices of polyhedra.


MA.912.G.7.4 Identify chords, tangents, radii, and great circles of spheres.


MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids.

Also assesses MA.912.G.7.4 and MA.912.G.7.6.

MC, FR

MA.912.G.7.6 Identify and use properties of congruent and similar solids.




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Geometry End-of-Course Assessment Body of Knowledge Geometry Standard 7 Polyhedra and Other Solids Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships

among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids and understand the properties of congruent and similar solids.

MA.912.G.7.7 Determine how changes in dimensions affect the surface area and volume of common geometric solids.


MC, FR

Body of Knowledge Geometry Standard 8 Mathematical Reasoning and Problem Solving In a general sense, mathematics is problem solving. In all mathematics, use problem-solving skills, choose how to approach a

problem, explain the reasoning, and check the results. At this level, apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. Learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.

MA.912.G.8.4 Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

MC

MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.




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Geometry End-of-Course Assessment Body of Knowledge Trigonometry Standard 2 Trigonometry in Triangles Understand how the trigonometric functions relate to right triangles, and solve word problems involving right and oblique

triangles. Understand and apply the laws of sines and cosines. Use trigonometry to find the area of triangles. MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) in terms of angles of right triangles.

MC, FR



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Documents

Geometry - Lake County and draw the basic elements of geometry using a straightedge, ... Review formulas for circumference and area of a circle. 3. ... How can you make a conjecture